Cartographer's Monthly - January 2021 - Featured: The Azimuthal Orthographic

The story of maps that push the limits of their two-dimensionality.

Maps, as everyone knows, all present one or another extreme abstraction of physical space. Their authors, each in their way, skillfully reduce the world and its terrible complexity to a harmless flat thing to be fingered on pages or screens. In the modern world especially, the utility of depicting a place as it is (done best with three-dimensional sculpture) pales in comparison to something false but portable, easily digestible, and serving well enough some very particular or immediate need.

The azimuthal orthographic is one projection that might be considered impractical and rather out of place in daily life. It is a product of a time long before our modern incuriosity took hold. Interestingly, this perspective from among the stars predates satellites or flying machines of any kind. Yet it is today the truest representation of a globe that is not itself a three-dimensional figure. With this precision, the orthographic aims not so much, like other maps, to reduce or expedite but rather beckons the viewer toward the fullness of understanding: such an expansion of consciousness as results from the intrepid exploration once undertaken by its progenitors.

And so shall we now explore the origins of this revolutionary map!

Azimuth derives from the Arabic السَّمْت ("as-samt"), meaning "the direction." It is a measurement of the angle between a pole or point of interest and two points on an equator or horizon. Any map that displays meridians as straight lines leading from a pole to the equator (or indeed any point of interest to any horizon) achieves this and is referred to as azimuthal. Within this category is the orthographic projection, "ortho" and "graph" being Greek for "straight" and "drawing," respectively. What characterizes the orthographic is that shapes approaching the horizon appear to fall away from the straight meridians intersecting at the center point. Also, our point of view is simultaneously close and infinitely far away (we have very good eyes).

The earliest known model of this type appeared in the second century B.C. in the series On Sizes and Distances by Hipparchus in which the astronomer proposed a method of acquiring approximate radii of the sun and moon. Though the texts themselves do not today survive, this process of measuring distant orbs is referenced in extant works of Ptolemy, Pappus of Alexandria, and others. It would form the basis for the construction of sundials accounting for latitude and longitude and just as soon aid in charting the actual curvature of the earth.

Illustration from Francois d'Aiguilon's Opticorum libri sex philosophis juxta ac mathematicis utiles (Six Books of Optics, useful for philosophers and mathematicians alike). A sphere in perspective is projected on the flat ground.

Largely untouched for centuries, the projection would be popularized in 1613 by Belgian cartographer Francois d’Aiguilon. Amid the pages of his six volume treatise on binocular vision, d'Aiguilon demonstrates how moving one's point of perspective relative to a globe causes its visible surface to shift relative to the horizon. In this way, up to half of an orb can be revealed when viewed from sufficient distance.

Various 20th century academics, too, would provide a more complete picture of the globe, finding corrections to be made in the records of antiquity and fine tuning Hipparchus' original approximations.

Fun fact: this particular photograph is upside down. NASA flipped it prior to publishing in order to satisfy earth dwellers' powerful "north is up" bias!

Now, with the advent of space travel, there is a certain renewed interest in the azimuthal orthographic. It is, perhaps, an awakening. A new challenge to see the world not only through the lens of powerful, narrowly focused abstractions, but to also lift our eyes now and then and engage in a wider world of visceral and beautiful reality.